Path curve: spline to pass through control points
To my best understanding NURBS curves do not precisely support what you wish to achieve and I could not find any options that would 100% bring the solution you wish for.
Option 1
if it's necessary that the spline must cross the vertices, you may want to try Bezier curves instead of NURBS curves. While you will lose the convenience of the NURBS curves (Bezier curves being a bit more tedious to edit), you can be sure that the curve crosses the vertex.
Option 2
If you don't want to use Beziers, but want to stay in NURBS curves instead, you can select the curve and navigate to &quot;Active Spline&quot; settings. From there you can reduce &quot;Order U&quot; to 2 and increase &quot;Resolution U&quot; to 12 or above, which will push the curve closer towards its control points. The trade-off is that you also lose the curvature from the curve itself, but you will have the curve following the control points.